End-to-end Surface Optimization for Light Control

2024-08-23

ACM Transactions on Graphics

AI Summary

This paper addresses the highly nonlinear inverse problem of freeform optical design by proposing an end-to-end differentiable optimization framework that jointly optimizes triangular mesh surface deformation and optical performance, directly driven by a target light-field distribution. Its key contributions are: (1) a patch-wise optimal transport update mechanism to mitigate local minima in gradient-based optimization; (2) integration of differentiable rendering with CNC-oriented geometric regularization, balancing optical accuracy and manufacturability; and (3) geometric-optical co-modeling via triangular mesh parameterization. Evaluated on multiple target images, the method achieves an average cosine similarity of 0.96 between simulated and target light fields. Physical prototypes fabricated from the optimized designs exhibit measurement results closely matching simulations, demonstrating substantial improvements in both design efficiency and fabrication feasibility.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Non-convex Optimization
• Machine Learning: Optimization

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Designing a freeform surface to reflect or refract light to achieve a target distribution is a challenging inverse problem. In this paper, we propose an end-to-end optimization strategy for an optical surface mesh. Our formulation leverages a novel differentiable rendering model, and is directly driven by the difference between the resulting light distribution and the target distribution. We also enforce geometric constraints related to fabrication requirements, to facilitate CNC milling and polishing of the designed surface. To address the issue of local minima, we formulate a face-based optimal transport problem between the current mesh and the target distribution, which makes effective large changes to the surface shape. The combination of our optimal transport update and rendering-guided optimization produces an optical surface design with a resulting image closely resembling the target, while the geometric constraints in our optimization help to ensure consistency between the rendering model and the final physical results. The effectiveness of our algorithm is demonstrated on a variety of target images using both simulated rendering and physical prototypes.

Problem

• Optimizing freeform surfaces for precise light control
• Ensuring manufacturability with geometric fabrication constraints
• Overcoming local minima via face-based optimal transport

Innovation

• End-to-end optimization for optical surface mesh
• Differentiable rendering model for light distribution
• Face-based optimal transport for shape updates